Layer transfer of films utilizing controlled shear region

ABSTRACT

A film of material may be formed by providing a semiconductor substrate having a surface region and a cleave region located at a predetermined depth beneath the surface region. During a process of cleaving the film from the substrate, shear in the cleave region is carefully controlled. According to certain embodiments, an in-plane shear component (KII) is maintained near zero, sandwiched between a tensile region and a compressive region. In one embodiment, cleaving can be accomplished using a plate positioned over the substrate surface. The plate serves to constrain movement of the film during cleaving, and together with a localized thermal treatment reduces shear developed during the cleaving process. According to other embodiments, the KIT component is purposefully maintained at a high level and serves to guide and drive fracture propagation through the cleave sequence.

CROSS-REFERENCE TO RELATED APPLICATION

The instant nonprovisional patent application is a continuation of andclaims priority to U.S. application Ser. No. 12/435,230 filed May 4,2009, which claims priority to U.S. Provisional Patent Application No.61/051,307, filed May 7, 2008 and incorporated by reference in itsentirety herein for all purposes.

BACKGROUND OF THE INVENTION

From the beginning of time, human beings have relied upon the “sun” toderive almost all useful forms of energy. Such energy comes frompetroleum, radiant, wood, and various forms of thermal energy. As merelyan example, human beings have relied heavily upon petroleum sources suchas coal and gas for much of their needs. Unfortunately, such petroleumsources have become depleted and have lead to other problems. As areplacement, in part, solar energy has been proposed to reduce ourreliance on petroleum sources. As merely an example, solar energy can bederived from “solar cells” commonly made of silicon.

The silicon solar cell generates electrical power when exposed to solarradiation from the sun. The radiation interacts with atoms of thesilicon and forms electrons and holes that migrate to p-doped andn-doped regions in the silicon body and create voltage differentials andan electric current between the doped regions. Solar cells have beenintegrated with concentrating elements to improve efficiency. As anexample, solar radiation accumulates and focuses using concentratingelements that direct such radiation to one or more portions of activephotovoltaic materials. Although effective, these solar cells still havemany limitations.

As merely an example, solar cells often rely upon starting materialssuch as silicon. Such silicon is often made using either polysiliconand/or single crystal silicon materials. Polysilicon material can also,depending on the size of single-crystal grains and degree ofcrystallinity, called multicrystalline, microcrystalline, ornanocrystalline. These materials will henceforth be called“polysilicon”, as opposed to single crystal (monocrystalline) materialwhich does not have numerous random crystal orientations and numerousgrain boundaries. Amorphous silicon is not a form of silicon commonlyused in wafered solar cells due to its poor carrier lifetime inthicknesses less than a few microns.

The materials for solar cells are often difficult to manufacture.Polysilicon cells are often formed by manufacturing polysilicon plates.Although these plates may be formed in a cost effective manner usingcrystallization furnaces, they do not possess optimum properties forhighly effective solar cells. In particular, polysilicon plates do notexhibit the highest possible efficiency in capturing solar energy andconverting the captured solar energy into usable electrical power.

By contrast, single crystal silicon (c-Si) has suitable properties forhigh grade solar cells. Such single crystal silicon is, however,expensive to manufacture and is also difficult to use for solarapplications in an efficient and cost effective manner.

Additionally, both polysilicon and single-crystal silicon materialssuffer from material losses during conventional manufacturing singlecrystal silicon substrates, where a sawing process is used to physicallyseparate thin single crystal silicon layers from a single crystalsilicon ingot originally grown. For example, inner diameter (ID) sawingprocess or wire sawing process eliminates as much as 40% and even up to60% of the starting material from a cast or grown boule and singulatethe material into a wafer form factor. This is a highly inefficientmethod of preparing thin polysilicon or single-crystal silicon platesfor solar cell use.

To overcome drawbacks of using silicon materials, thin-film solar cellshave been proposed. Thin film solar cells are often less expensive byusing less silicon material or alternative materials but their amorphousor polycrystalline structure are less efficient than the more expensivebulk silicon cells made from single-crystal silicon substrates.

From the above, it is seen that techniques to manufacture suitable highquality single crystal silicon sheets with low cost and highproductivity are highly desired.

BRIEF SUMMARY OF THE INVENTION

A film of material may be formed by providing a semiconductor substratehaving a surface region and a cleave region located at a predetermineddepth beneath the surface region. During a process of cleaving the filmfrom the substrate, shear in the cleave region is carefully controlled.According to certain embodiments, an in-plane shear component (KII) ismaintained near zero, sandwiched between a tensile region and acompressive region. In one embodiment, cleaving can be accomplishedusing a plate positioned over the substrate surface. The plate serves toconstrain movement of the film during cleaving, and together with alocalized thermal treatment reduces shear developed during the cleavingprocess. According to other embodiments, the KIT component ispurposefully maintained at a high level and serves to guide and drivefracture propagation through the cleave sequence. In one embodiment, thehigh KIT component is achieved by adiabatic heating of silicon throughexposure to E-beam radiation, which imparts a highly abrupt thermalgradient and resulting stress at a precisely defined depth in thesilicon.

Embodiments of the present invention relate generally to layer transfertechniques for forming thick films. More particularly, the presentinvention provides a method and device for low or even implant freelayer transfer of thick films for solar cells. Merely by example, it isapplied to cleave thick films along a crystallographic plane of singlecrystal silicon substrate. But it will be recognized that the inventionhas a wider range of applicability.

Many benefits can be obtained by implementing the present invention. Ina preferred embodiment, single crystal silicon ingot substrate with asurface plane in an {111} or {110} crystallographic plane can beselected. Thus, the ion implantation process for creating cleave regioncan be mostly eliminated or limited to form a cleave initiation regionwith a portion of peripheral region. This substantially simplifies thelayer transfer process, reduces system energy cost and increasesproductivity.

In certain embodiments, the process is divided into (i) an initiationprocess utilizing a higher implant dose (the initiation dose) toinitiate a fracture in a relatively small area of the silicon ingotsubstrate (the initiation region), and (ii) a propagation process thatextends the initiated crack tip through the remainder of the siliconingot substrate to release the thick film (the propagation region).Since the propagation process must extend the initiation region throughthe majority of the surface area of the thick film to be released, thisprocess should operate reliably with a small implant dose, and perhapswithout any dose. This is called the propagation dose, and the totaldose needed for the process would therefore be the weighted area averageof the initiation and propagation dose. For example, if the initiationarea is 1% of the total area and utilizes 6×10¹⁶ cm⁻² hydrogen while thepropagation area utilizes 1×10¹⁶ cm⁻² hydrogen, the total effective doseis 0.01*6×10¹⁶ cm²+0.99*1×10¹⁶ cm⁻² or 1.05×10¹⁶ cm⁻². Reducing oreliminating the propagation dose will have a first order effect on thetotal dose requirement for this cleaving process.

Lowering of the dose in turn depends on (i) optimizing the effect of theimplanted hydrogen to maximize its cleave guiding action and (ii)optimizing the cleave process by generating the right stress intensityconditions at the crack tip to keep the cleave front within the desireddepth without breaking or cracking the film. Embodiments in accordancewith the present invention are directed to optimizing the mechanicalconfiguration during the cleave propagation process.

In one embodiment, the cleave initiation region can be created in apatterned implantation by irradiating high energy ionic particles withcontrolled dosage generated using a linear accelerator. In certainembodiments, the present invention provides a mechanical moment loadingwith a force loading (generated through an appropriate thermal treatmentprocess and/or mechanical forces) to generate a stress gradient suchthat a substantially zero shear region can be formed despite the naturaltendency of the mechanical configuration to generate mixed-mode loading.In other embodiments, the externally applied energies generatecontrolled mixed-mode loading conditions sufficient to allow propagationalong a desired cleave plane.

Utilizing embodiments of the present invention, a high quality thickfilm crystalline material having a thickness ranging from a few tens ofmicrons to a few hundreds of microns, can be produced with kerf losssubstantially lower than possible utilizing conventional techniques. Theresulting single crystal silicon thick films are particularly suited foruse in high efficiency (20% or higher) photovoltaic cells. Someembodiments can utilize existing manufacture processing systems andtechniques, and take some advantage of certain newly developedtechniques for manufacturing thin wafer/substrate for varioussemiconductor device applications. More details about variousembodiments of the present invention can be found in the descriptionbelow.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a simplified schematic view of the general case ofpropagation.

FIG. 2 is a simplified diagram showing a formation of a cleaveinitiation region by patterned implanting high energy particlesaccording to an embodiment of the present invention.

FIG. 3A shows a simplified cross-sectional view of an apparatus forcleaving including a constraint plate.

FIG. 3B shows simulation results of the stress of the film resultingfrom cleaving utilizing a constraint plate.

FIG. 4 plots for use of film displacement loading, several values as afunction of distance (in μm) of the centroid of the cleaved zone fromthe tab edge of the substrate during crack propagation.

FIG. 5 plots for thermal shear, several values as a function of distance(in μm) of the centroid of the zone from the tab edge of the substrateduring crack propagation.

FIG. 6A plots cleave energy versus temperature differential at anapplied pressure of 42 kPa.

FIG. 6B plots KII/KI ratio versus temperature differential at theapplied pressure of 42 kPa.

FIG. 7 shows the fully loaded pressure just prior to thermal loading andcrack propagation.

FIG. 8A shows the resultant thermal profile at the end of the heat soak.

FIG. 8B shows the resultant thermal profile at the end of the coolshock.

FIGS. 9A-D shows the heating/cooling cleaving sequence for cleavingthree zones and the crack propagation time sequence following theapplication of pressure.

FIG. 10 shows the energy profile resulting from application of a thermalcleaving process.

FIG. 11 shows the electron range into silicon and germanium as afunction of electron energy.

FIG. 12A-C shows the resultant film stress and cleave conditions uponmoment loading, at the start and near the end of an adiabatic heatingpulse.

FIG. 13 plots energy density versus depth into silicon resulting fromthe adiabatic heating resulting from application of an electron beamover a time period.

FIG. 14 is a simplified cross-sectional view showing cleaving by thegeneration of moments M₂ and M₃ by direct application of force to edgesof a clamped substrate.

FIG. 15 is a simplified cross-sectional view showing cleaving by thegeneration of moments M₁-M₃ and forces P₁-P₃ resulting from theapplication of thermal energy to a clamped substrate.

FIG. 16 is a simplified schematic view showing cleaving by thegeneration of moments M₁, M₂, and M₃ resulting from the application ofsonic energy to a clamped substrate.

FIG. 17 is a simplified schematic view showing cleaving by thegeneration of moments M₁, M₂, and M₃ resulting from the localapplication of sonic energy to a clamped substrate.

FIG. 18 is a simplified process flow showing the steps of an embodimentof a process in accordance with the present invention.

DETAILED DESCRIPTION OF THE INVENTION

Particular embodiments of the present invention provide a method anddevice for layer transfer of thick films for solar cells. Merely byexample, it is applied to cleave thick films along a crystallographicplane of single crystal silicon substrate. But it will be recognizedthat the invention has a wider range of applicability. For example,other materials such as Germanium, Gallium Arsenide (GaAs), GalliumNitride (GaN), or Silicon Carbide (SiC) could be subjected to thecleaving process to release films of materials for solar,opto-electronic or semiconductor applications.

As discussed in background section, the growth of silicon based solarcells relies on driving down a bottleneck for cost in waferingkerf-loss. Traditional sawing, or adopting recently reported waferingtechnologies (such as multi-wire saw, spark cutting, laser cutting, orplasma cutting) that render thick films suitable for solar cells, mayexhibit limited usefulness due to one or more of the following issues:high kerf loss high, slow cutting speed, and lack of manufacturability.

A solution is to use a high energy ion beam to create a cleave region ata desired thickness beneath the substrate surface, then perform a layertransfer process to free the thickness of film from remaining substrate.However, use of only implanted ions to create a cleave regionsusceptible for cleaving, may require a high ion dose and an extendedimplanting area. Moreover, such reliance upon implanted ions may resultin higher surface roughness, added cost with high ion dose and lessproductivity, and potentially lower yields. Depending upon theembodiment, these and other limitations are overcome using the presentmethod and structures.

According to particular embodiments of the present invention, cleavingof a film of material may be accomplished with substantially reducedimplantation of ions, or possibly no implantation at all, utilizing acleaving process that carefully controls the shear conditions during thecleaving. In an embodiment, a film of material may be formed byproviding a semiconductor substrate having a surface region, aperipheral region, and a cleave region at a predetermined depth beneaththe surface region. For purposes of the instant patent application, theterm “cleave region” does not necessarily denote a region that hasreceived radiation or implanted ions, but rather refers to a region thatmay be separated from the substrate following the application ofradiation and/or implanted ions and/or suitable external cleavingenergies.

A cleave initiation region may be defined within a portion of theperipheral region and a vicinity of the cleave region. The cleaveinitiation region may be formed by subjecting the region to a thermal,chemical, electrical, and/or mechanical process to spall or release asection of the film within the initiation region.

In one embodiment, initiation cleaving is accomplished by subjecting thecleave initiation region to a localized thermal treatment, so that acleave front can be initiated within this region and propagates to theperiphery of the initiation region where the dose is lower and does notpromote further propagation. The general film release process can thencontinue to propagate the initiated film from the existing cleave frontthrough the remainder of the substrate.

FIG. 1 is a simplified diagram illustrating a side view of asemiconductor substrate having a cleave region at a predetermined depthbeneath a surface region according to an embodiment of the presentinvention. This diagram is merely an example, which should not undulylimit the scope of the claims herein. One of ordinary skill in the artwould recognize many variations, alternatives, and modifications.

As shown in FIG. 1, a semiconductor substrate 1700 is provided having asurface region 1702 and a peripheral region 1704. In addition, a cleaveregion 1706 is provided. This cleave region is in essence a virtualplane or layer located at a predetermined depth d beneath the surfaceregion 1702, and is used to define a thickness of thick film 1720 to bedetached from the semiconductor substrate 1700. In one embodiment, thesemiconductor substrate has a thickness substantially larger than thedepth d. In a specific embodiment, the semiconductor substrate is singlecrystal silicon material for use in a photovoltaic solar cell. In aspecific embodiment, the silicon substrate has a surface plane that isselectively in a {111} or {110} crystallographic plane (a certain smallmiscut angle of less than about 1° or less than about 3° may exist). Ina specific embodiment, the cleave region defined is substantiallyparallel to the surface region. Since the cleaving action isenergetically easier along the {111} plane followed by {110} plane thanin the traditional {100} plane, it is desirable to orient the materialto be cleaved to coincide the surface to be cleaved with a lower surfaceenergy crystallographic cleave plane. More detailed description oftechniques for selecting certain orientation of the silicon boule forslicing or cleaving can be found in the U.S. Provisional PatentApplication to Francois J. Henley titled “METHOD AND DEVICE FOR SLICINGA SHAPED SILICON INGOT USING LAYER TRANSFER,” (Attorney Docket No.:018419-025600US), commonly assigned, and hereby incorporated byreference herein.

FIG. 1 also shows the formation of a cleave initiation region by patternimplanting high energy particles according to an embodiment of thepresent invention. This diagram is merely an example, which should notunduly limit the scope of the claims herein. One of ordinary skill inthe art would recognize many variations, alternatives, andmodifications.

As shown in FIG. 1, a portion of the peripheral region 1704 can beassociated with a predetermined patterned region (not shown directly inthe cross-sectional view of FIG. 1) within the surface region 1702. Inone embodiment, the selected portion of the peripheral region is withinan edge vicinity of the cleave region 1706.

Then the patterned region of the surface region 1702 is exposed to ahigh energy ion beam 1740, for example H+ ions with energy level of 1MeV or more using a linear accelerator. In one embodiment, the area ofthe patterned initiation region is limited to 1-3% of the totalsubstrate surface area (e.g., 2-5 cm² or less for a 125 mm×125 mm sizedsubstrate), so that the ion particle dose is well controlled minimizeenergy costs of the system and enhance productivity of the thick filmcleaving process.

The high energy ions are implanted beneath the surface region to reach aregion within the vicinity of the cleave region 1706. The penetrationdepth of the ions is dependent on the energy level, and can becontrolled to a desired value that determines a depth d of the cleaveregion. The implanted ions slow down within the crystal lattice bytransferring kinetic energy to the lattice in the form of ionization(electronic braking), and small amount of atomic damage by displacingatoms (nuclear stopping).

During the final phase (about 2-5% of the total range), the ionsinteract substantially more with the crystal lattice under nuclearstopping, and a thin region of relatively high stress and damageslattice bonds is formed to define a cleave initiation region 1708. Asshown, the formed cleave initiation region 1708 is a small planar regionextending from a portion of the peripheral region 1704 toward within thecleave region 1706. Since the patterned implantation is performed byirradiating ionic particles within an area less than 1-3% of total areaof surface region, this initiation dose can be higher than thepropagation dose. This allows the averaged area dose to be maintainedlow for enhanced productivity. Of course, there can be manyalternatives, variations, and modifications.

Substantially Zero Shear Region

Certain embodiments of the present invention seek to modify the cleavingconfiguration to reduce, eliminate, or control the shear mode II stressintensity factor (KID at the tip of a propagating cleaving fracture.Under such conditions, the cleaving action is allowed to progress alongthe desired cleave plane.

While the condition KII=0 is an ideal condition for cleaving direction,there is a certain range of KII within which the cleaving will followeither a crystallographic cleave plane or a plane of hydrogen implantdosage. Thus, where conditions allow for maintenance of KIT within alimited range around zero, the cleaving action can desirably continue tofollow a cleave plane.

The following discussion address general Linear Elastic FractureMechanics (LEFM) equations that may govern cleaving according toembodiments of the present invention. This analysis assumes a large-areatile, where the film is much thinner than the remainder of the silicontile.

The mechanical configuration following the initiation process is shownin FIG. 2. Specifically, a thick film of thickness h is partiallyreleased from the rest of the silicon ingot substrate having thicknessH. Due to the much larger dimensions of the substrate relative to thecleaved material, h<<H and the tile moment and forces M₂, P₂ and M₃, P₃are understood to be very small. The source of stress intensity seen atthe crack tip is thus dominated by M₁ and P₁, the moment and forcecoupled to the partially released thick film.

A basic concept of embodiments of the present invention is the hydrogencleave plane. The hydrogen cleave plane (H-plane) affects the cleavingaction through stress and layer weakening effects. Specifically, theH-plane can be used both as an initiating layer at higher doses, and asa guiding or propagating layer when the dose is lower. The action of theH-layer is different within these two dosage regimes.

One effect upon cleaving action of the end-of-range (EOR) hydrogenimplant layer, is the reduction in fracture strength around the cleaveplane. Such reduction in fracture strength can be caused by bond damageand by stress induced by the presence of the hydrogen itself. Both ofthese considerations can lower the energy needed to create a new surfaceduring cleaving.

The energy needed to create a new surface during cleaving, is hereafterreferred to as the surface energy (γ). In unimplanted single crystalsilicon, the surface energy is about 1.2 J/m² for the {111} orientation,although fracture toughness in silicon is sometimes reported as 4-6 J/m²and includes effects such as lattice trapping to give an effectiveenergy to produce a new surface. For the following analysis of siliconat {111} orientation, a surface energy of 1.2 J/m² per surface (2.4 J/m²total) will be assumed.

By contrast, the value of the modified surface energy (γ′) along animplanted cleave plane can be substantially lower, perhaps by a factorof 5 or more. The surface energy value γ′ of the effective cleave planeis related to the unimplanted surface energy (γ) according to thefollowing relation:

γ′=α_(H) ²*γ  (1)

where α_(H) is a factor between 0 and 1 that serves to quantify thereduction in cleave energy due to hydrogen embrittlement. The α_(H) termaccounts for all of the effects necessary to yield an accuraterepresentation of all of the stress and bond damage effects. α_(H) isexperimentally determined as a function of cleave energy, dose, implantthermal conditions, and post-implant thermal conditions.

If the H-dose embrittlement effects are proportional to stressintensity, it may follow that cleave energy is related quadratically todose as follows. For relatively low doses of less than about 3-4×10¹⁶cm⁻²:

α_(H)=1/(1+k _(H)*φ)  (2)

where k_(H) is a constant to be determined experimentally, and φ is thehydrogen dose.

Substituting equation (2) into equation (1) yields:

γ′=[1/(1+kH*φ)]²*γ  (3)

Since the cleaving energy is a fundamental parameter in linear elasticfracture mechanics, the correlation between implant dose and energyallow accurate prediction and modeling of cleaving action.

Two surfaces are created during the cleaving process. Thus the cleaveenergy release rate (G′) is related to the surface energy as follows:

G′=2*γ′=2*α_(H) ²*γ  (4)

Depending on the embrittlement factor (α_(H)), G′ can change from about2.4 J/m² to substantially less within the cleave plane. For example, inan experiment involving a 50 μm thick single crystal silicon film, acrack in a cleave plane formed by a H implantation dose of 2-8×10¹⁶ cm⁻²showed that for H-doses higher than about 4-6×10¹⁶ cm⁻², there is ameasurable lowering of the cleave energy (α_(H) ²<1) as measured by adouble-cantilever beam mechanical configuration.

Lower cleave energy can have a guiding effect to keep the cleave planewithin the weakened layer during propagation. This is because the energybarrier to branching from the cleave plane will be higher if α_(H) islower. For example, a high dose implant may result in sufficientlowering of the cleave energy within the implant, that the film maysimply peel off of the substrate.

For cleave planes with lower hydrogen doses (less than about 4×10¹⁶cm⁻²), it has been experimentally determined that α_(H) ²˜1. With thecleave energy essentially having intrinsic cleave energy values, cleaveguiding at lower doses is thus mostly dominated by the implantedhydrogen compressive stress profile that helps keep the cleave frontpropagating along the cleave plane. Specifically, a guiding effect isthe shear force generated by the in-plane compressive layer that isgenerated when the cleave front moves away from the center of thecompressive stress profile. Any deviation of the cleave front depth awayfrom this center point of compressive stress, will tend to generate anin-plane (KII) shear force having a polarity that tries to maintain thecleave front propagating parallel to and within the cleave plane over arange of shear stress intensity values (non-zero KID. Thus, if thecleave front starts moving up to the surface, a positive (K_(II)) shearforce will guide the cleave front lower towards the center. Conversely,if the cleave front starts moving lower into the tile, a negative K_(II)shear force will guide the cleave front higher towards the center.

This phenomenon occurs because any non-zero KII generated duringcleaving will tend to guide the fracture plane away from the cleaveplane so as to minimize KII. This effect can be cancelled to some extentby the shear generated by the cleave layer that is generated in theopposite direction. The result is a net offset in cleave depth thatbecomes the new cleave depth where KII=0.

This slight movement of the cleave depth has been experimentallyobserved, and the maximum shear that the cleave layer can absorb isrelated to the compressive stress level present at the cleave plane andthe straggle (Rp) of the implant defining the cleave plane. Once theshear stress level is higher than this critical level, the cleave frontwill jump out of the cleave plane and cleave failure will occur.

It is therefore a potentially important design consideration to have acleaving configuration that minimizes the induced KIT shear forces, inorder to allow controlled cleaving at the desired depth with lowpropagation doses. The effect can be modeled by a capture range of KIIstress intensities within which the cleave propagation directioncontinues to lie parallel and close to the KII˜0 fracture propagationplane.

The upper and lower limits of KII stress intensity factors where cleavedirection control is lost, are defined as A_(KII−) and A_(KII+). Theseparameters are important to the design of the cleaving process, sincelow capture ranges would mean that the cleave plane can easily branchand cause cleave failure.

Determining the A_(KII−) and A_(KII)+ factors as a function of dose andimplant/anneal conditions are also relevant to the design of thecleaving system. An estimated A_(KII−) to keep the propagation with amixity (KII/KI) of −0.779 (the mixed-mode stress intensity ratio of afilm bending mode M₁ with no film stress P₁) for {111} silicon withα_(H) ²˜1, is about −0.18 MPa-m^(1/2).

Cleave failure is essentially defined as the unwanted branching of thecleave plane, usually resulting in fractured films. Avoidance ofunwanted branching of the cleave plane is thus a consideration in thedesign of cleaving techniques. Other factors found to affect unwantedbranching include crystal orientation and implant dose and depth andtemperature profile, for example.

Other effects have been found to be important. For example, forsingle-crystal silicon, thermal energy injected within the vicinity ofthe cleave plane and used to generate P₁ cleaving stresses, will beaffected by the fact that the implanted cleave plane has a substantiallylower thermal conductivity over unimplanted single-crystal silicon. Thislower thermal conductivity is a result of the hydrogen implant damageand will tend to modify the temperature profile, which in turn willmodify the cleaving stresses.

A series of closed-form equations have been developed to investigatecleaving behavior. Development of these equations assumes that a startercrack resulting from cleave initiation, is present at a depth of (h)into the substrate, thereby defining the thickness of the cleaved film.In many of the examples, h=50 μm, but any film thickness is allowed inthe equations. The models assume a 5 mm detached film length (named c orsometimes L). The geometry is two-dimensional, meaning that the width wdoes not change as the cleaving occurs along a line.

The crack opening force mode (KI), and the in-plane shear force mode(KII), are important parameters for modeling the cleaving process. Itwould be expected that the resultant conditions leading to crackextension and propagation would match silicon or any other material ifthe known fracture energy for that cleaving configuration is utilized.For example, the fracture condition is known to occur in single crystalsilicon when G′ exceeds 2*γ′, about 2.4 J/m² for an unimplanted layer.

The threshold for fracture propagation is defined as follows:

$\begin{matrix}{G = {\frac{1}{E_{1}}\left( {K_{I}^{2} + K_{II}^{2}} \right)}} & (5)\end{matrix}$

where E′=the plane strain equation defined as E′=E/(1−υ)²), and, for allpurposes of this document, G is G′ and generally related to the cleaveplane by equation (4):

G′=2*γ′=2*α_(H) ²*γ  (4)

FIG. 2 shows the general case of the propagation problem. Substitutingequation (4) into equation (5) yields the following solution for KI andKII:

$\begin{matrix}{G^{\prime} = {\frac{1}{2\overset{\_}{E}}\left\lbrack {\frac{P_{1}^{2}}{h} + {12\frac{M_{1}^{2}}{h^{3}}} + \frac{P_{2}^{2\;}}{H} + {12\frac{M_{2}^{2}}{H^{3}}} - \frac{P_{3}^{2}}{h + H} - {12\frac{M_{3}^{2}}{\left( {h + H} \right)^{3}}}} \right\rbrack}} & (6)\end{matrix}$

Where P_(n) and M_(n) are the forces and moments respectively, acting oneach of the members.

The KI and KII factors then take the form:

$\begin{matrix}{{K_{I} = {{\frac{P}{\sqrt{2{hU}}}\cos \; \omega} + {\frac{M}{\sqrt{2h^{3}V}}{\sin \left( {\omega + \gamma} \right)}}}},{K_{II} = {{\frac{P}{\sqrt{2{hU}}}\sin \; \omega} - {\frac{M}{\sqrt{2h^{3}V}}{{\cos \left( {\omega + \gamma} \right)}.}}}}} & \left( {7,8} \right)\end{matrix}$

Where the parameters are derived from the forces, moments and geometryas described in detail by Hutchinson and Suo, “Mixed Mode Cracking inLayered Materials”, Advances in Applied Mechanics, Vol. 29 (1992), whichis incorporated by reference in its entirety herein for all purposes.

If the thickness of the remaining substrate (H) is assumed to be verylarge compared to the film thickness (h), the above equations (7, 8) canbe simplified and collapsed into equations (9, 10) by the following:

γ(angle)=0

P=P1

M=M1

U=1

V= 1/12

ω=52.07 degrees

η=h/H˜0

All C constants are zero

$\begin{matrix}{{K_{I} = {\frac{1}{\sqrt{2}}\left\lbrack {{{Ph}^{{- 1}/2}\cos \; \omega} + {2\sqrt{3}{Mh}^{{- 3}/2}\sin \; \omega}} \right\rbrack}},{K_{II} = {\frac{1}{\sqrt{2}}\left\lbrack {{{Ph}^{{- 1}/2}\sin \; \omega} - {2\sqrt{3}{Mh}^{{- 3}/2}\cos \; \omega}} \right\rbrack}},} & \left( {9,10} \right)\end{matrix}$

Equations (9, 10) will be used to derive the various configurations ofthe cleaving approaches for the case where M₂, P₂ and M₃, P₃ are zero.The only change in the equation based on the configuration is to includethe appropriate force (P) and moment (M) relationships for theparticular loading conditions. The case where M₂, P₂ and M₃, P₃ are notzero is discussed later.

Cleave Configurations Leading to KII Cancellation

The general equations 9 and 10 show that forces and moments imparted tothe film will generate KI and KIT stress intensity factors at the cracktip as described in the equations. The film force P is the force perunit width imparted to the film and related to film stress at the cracktip area as P=6*h. The moment is the moment impressed onto the film thatgenerates M at the crack tip. That the M and P relation is additive inequation 9 but subtractive in equation 10, suggests that application ofP and M can add in KI while subtracting in KII. Therefore, if the momentM and film stress force P are chosen correctly, the condition ofsimultaneously achieving crack extension while KII is cancelled (zero)would assure that the propagating crack has the greatest tendency topropagate along the cleave plane. This optimized set of conditions wouldallow low or zero dose cleave plane operation, and even allow controlleddepth guiding through active control of M and P as a function of theactual cleave depth achieved during crack extension. Such reduced or nodose conditions, and control over the depth of cleaving are among thesignificant benefits achieved according to embodiments of the presentinvention.

Coordinate System Used in the Models

To quantify the various configurations, a coordinate system was definedwith the cleave plane along the X direction (positive X to the right),the thickness of the film along the Y-direction (positive in the updirection), and the Z direction is positive out of the surface. Thiscoordinate system is used in the Finite Element Analysis (FEA) code.Software available from Ansys, Inc. of Canonsburg, Pa. (hereafter theAnSys software) was used to model the crack propagation system andincluded thermal and mechanical parts that interacted with a cohesivezone model (CZM) of the interface. The CZM code allowed thedetermination of conditions under which the applied stresses and momentswould propagate the fracture.

The configuration of FIG. 2, where the detached, initiated film is tothe left, was entered into the AnSys software. The results aresummarized in the following sections and show the KII cancellationaction resulting from different loading (P and M) configurations.

Moment Application Conditions

The moment applied to the film was a bending of the film away from therest of the substrate. Such bending will generate KI and KII conditionsthat tend to break the film. If a pure moment (P=0) is used, the KI andKII will change depending on the moment value, but will have a constantratio (KII/KI) of −cos(ω)/sin(ω) or −0.78 since ω is unchanging with avalue of 52.07 degrees. This ratio is defined as the mixity of thestress intensity, and its value determines the tendency for thepropagating front to change in thickness (the Y-direction). The momentapplication is therefore negative in mixity (snapping the film), andproportional to the bending of the film as experienced by the crack tip.

There are stable, metastable, and unstable methods of applying momentsto a film. The major configurations are summarized below.

Constant Displacement Loading

A constant displacement applied to a film at a certain distance awayfrom the crack tip is considered a stable loading configuration, sinceany crack extension will reduce the applied moment. The displacement isincreased to reload the crack tip and the propagation process canresume. A blade or other means of developing a fixed distance in both Xand Y at a point beneath the pre-cleaved film would develop a constantdisplacement load.

Constant Force Loading:

A constant force applied to a film at a certain distance away from thecrack tip is considered an unstable loading configuration since anycrack extension will increase the applied moment. This will usuallyresult in uncontrolled crack extension and thus is not a preferredloading configuration.

Constant Moment Loading

A constant moment loading on a film can be developed using certainconfigurations as described here. One advantage of this configuration isthe ability of the system to stay to a desired moment loading withoutactive assistance. If a crack extension occurs with an application of asecond load, for example, the system will continue being loaded with thesame moment. This configuration is to be avoided if the moment is chosento exceed the fracture strength of the material, since uncontrolledcrack extension can occur.

The film bending moment can be applied either statically orquasi-statically or in a dynamic manner such as exciting the filmultrasonically in resonance or out of resonance. In all cases, themoment loading M imparted to the crack tip, according to certainembodiments of this invention, is designed to increase the KI and KIIstress intensity factors using ultrasonic motion, displacements, andforces to a design point to allow controlled crack propagation along adesired cleave plane.

If the guiding of the cleave plane is sufficient (high A_(KII−) andA_(KII)+), then there would be no reason to add P to the configurationand a threshold crack extension along the desired cleave plane ispossible. This would occur if the A_(KII)− and A_(KII+) are sufficientlyhigh to counter the inherent KII/KI mixity of −0.78 of this momentloading configuration. This does not occur naturally in silicon but withan optimized cleave plane, this may be a sufficient loadingconfiguration to accomplish film detachment.

Constant Moment Loading Example Using Pressure and a Constraint Plate

According to particular embodiments, a plate positioned over thesubstrate may be utilized to constrain movement of the film separatedduring the cleaving process. In particular, the presence of theconstraint plate may serve to reduce the in-plane shear mode component(KII) during cleaving when a second loading is used.

In certain embodiments, a constraint plate according to the presentinvention may be employed in combination with a source of pressureapplied from the side, to accomplish cleaving of a film from asubstrate. FIG. 3A shows a simplified schematic view of such anembodiment of the present invention.

Specifically, constraint plate 400 is disposed over a front surface of asubstrate or tile 404 having its back surface supported on a tray notshown. Constraint plate 400 is separated from the underlying substrateor tile 404 by a distance Wo. Application of pressure (for example froma gas jet) to the side of the substrate 404, results in the pre-detachedfilm 412 being pushed away from the remaining substrate and imparting aconstant moment load. During this process, movement of film 412 isconstrained by the presence of the plate 400.

FIG. 3B shows simulation results of the stress of the film resultingfrom cleaving utilizing such a constraint plate according to anembodiment of the present invention. The picture in FIG. 3B shows apre-detached film of length 5 mm and thickness of 50 um moved(exaggerated) up and against the constraint plate using a few psi ofpressure. The pressure moves the film towards a constraining platesituated above the surface. Here, a separation (Wo) of 50 um is used inthe modeling.

An advantage offered by the configuration of FIG. 3A is its simplicityand the relative ease of generating the stresses necessary to propagatethe fracture. The use of the constraint plate confers the benefit thatno blade is needed to perform the cleaving. Alternatively, if aconstraint plate is used in combination with a form of displacementcleaving (for example, a blade), the frictional forces on the blade canbe reduced to arbitrarily low values.

An embodiment of a constraint plate in accordance with the presentinvention can utilize a force such as a vacuum force or an electrostaticforce to attract and hold the cleaved film. In a particular embodiment,the constraint plate can be porous, such that a positive pressure can besupplied to create an air bearing surface supporting the attractedcleaved film thereby allowing translation of the substrate/constraintplate relative to one another as the cleaving proceeds across thesubstrate.

An issue with the configuration of FIG. 3A (as with the other momentloading configurations) is its high negative KII mixity. This can tendto snap the film.

In this configuration, P and M of equations (9, 10) are as follows:

P=0 (no stress is imparted on the film in the X direction)

M=p*c ²/(4*k)  (11)

Where M is a moment per width, and thus has the dimension of force,rather than force*distance. p is the pressure differential impartedbelow the film, and c is the distance between the point where the filmseparates from the constraint plate to the crack tip.

Factor k of equation (11) is a parameter that may change depending onthe friction between the constraint plate and the film. As will beshown, many of the basic elements of embodiments of the presentinvention are independent of k.

Different pressure loading configurations have a corresponding k thatcan be calculated. An unconstrained film (no top plate) will have k=½,while a circular blister will have k=2. Using a constraint plate, k isdependent on the method in which the film is being secured onto theconstraint plate. Assuming that the film is constrained only in the Y(vertical) direction and frictionless, simulation with the AnSyssoftware shows the k factor to be about sqrt(2) and therefore this willbe used in the derivation of the equations. In the KII=0 relationships,the k factor does not play a role, and thus any error caused by adifferent k factor from 1 to 1.5 is considered small.

The KI and KII equations (9, 10) are thus transformed into equations(12, 13):

KI=6^(1/2) *p*c ²*sin(ω)/(4*k*h ^(3/2))  (12)

KII=−6^(1/2) *p*c ²*cos(ω)/(4*k*h ^(3/2))  (13)

Again, the KII/KI mixity will be independent of pressure and thus thefilm will tend to snap off with reasonable geometries due to the highlynegative KII.

The pressure p at which the crack will extend is:

p=[16*k ² *E′*γ′*h ³/(3*c ⁴)]^(1/2)  (14)

Assuming k=sqrt(2), unimplanted silicon, c=3.3 mm (the crack length thatexperiences the pressure p), and h=50 um, the critical pressure p isabout 52 kPa, about 0.5 atmospheres of gauge pressure.

Simulation runs with the AnSys software have confirmed that cleavepropagation occurs at a about 51 kPa using the parameters above. Theequations are therefore considered fairly accurate for modeling stressintensity factors and predicting the onset of crack extension.

The AnSys software was also used to extract the Mode I (crack opening)and Mode II (in-plane shear) cleave energies, designated herein D1 andD2 respectively. Specifically, these cleave energies are extracted atthe time of CZM debonding (cleaving). This extracted data can show theefficacy of the KII cancellation approaches.

To test the AnSys software, displacement and shear cleaving loads wereused to compare with the closed form solutions of M-only and P-onlycleave configurations. In all models, the cleave energy is 2.4 J/m²,Young's Modulus is 187 GPa, the thermal expansion coefficient is 2.5ppm, and Poisson's Ratio is 0.272.

In the moment-only test, a 500 um displacement of the 5 mm film was usedto measure the cleave energies D1 and D2. FIG. 3 plots several values asa function of distance (in μm) of the centroid of the cleaved zone fromthe tab edge of the substrate. FIG. 4 shows a mixity of about 0.6, andtotal cleave energy (D1+D2) of about 2.2 J/m². This slightly lower valueof the mixity as compared with the expected value of 0.78, is a resultof the thin bottom silicon used in the model. As the bottom siliconthickness is increased, mixity rises asymptotically to the 0.78 value.

In the P-only test, thermal shear cleaving measured the cleave energiesD1 and D2. FIG. 4 plots several values as a function of distance (in μm)of the centroid of the zone from the tab edge of the substrate. FIG. 5shows a mixity of about 2, and cleave energy of about 2.2 J/m². Thisslightly lower value of the mixity as compared with the expected valueof 2.2 for pure shear cleaving, is a result of the thin bottom siliconused in the model. As the bottom silicon thickness is increased, mixityrises asymptotically to the 2.2 value.

Cleaving Propagation by Displacement Loading

According to certain embodiments, cleaving can be initiated bydisplacement loading—pulling on the film during cleaving to a specificdistance in a direction away from the substrate surface. An example ofsuch a cleaving approach utilizes insertion of a blade to pull the filmaway from the substrate during cleaving. In such embodiments P=0 andM=Fw*c, where Fw is the force per unit width (into the paper) and c isthe crack distance in from the crack tip in which the load is applied.

Under these loading parameters, the KI and KIT equations are:

KI=6^(1/2) *fw*c*sin(ω)/h ^(3/2)  (15)

KII=−6^(1/2) *Fw*c*cos(ω)/h ^(3/2)  (16)

The force necessary to cleave is related to γ′ by the following:

Fw=[E′*h ³*γ′/(3*c ²)]^(1/2)  (17)

A negative KII means that the crack will tend to deflect upward,snapping off the film during attempts to bend the film upwards usingthis configuration.

In one experiment, a relatively thick blade of 50 um (a piece of acleaved silicon film) was able to extend a crack when pushed under thepartially cleaved film. This experiment involved an implant dose levelof on the order of 2-3×10¹⁶ cm⁻². A 2 mm extension was observed, but theinserted piece ended up binding to the film, and was not able to bemoved thereafter. Since the binding is very sensitive to surfacefriction, blade thickness and other parameters, this technique may workbut it would do so without the benefit of achieving KII=0. In otherwords, without KII cancellation, a blade or other form of displacementcleaving will rely to a greater extent on a weaker cleave plane orcleave plane compressive stresses to compensate for the non-zero KIT inthis configuration.

A thin diamond like carbon (DLC) coated blade used with an ultrasonicapproach to breaking static friction/binding, could allow the bladetechnique to be used. Acoustic energy is applied through the mechanicalblade and delivered to the tip region as the tip region is pushed inwardalong the already cleaved or initiated region. In one embodiment, theacoustic energy can be generated using an ultrasonic energy source or amegasonic energy source that operably couples to the mechanical blade.The acoustic energy reaching the tip region may cause ultrasonicexcitation of the semiconductor substrate material at the cleave frontor the vicinity of the tip region. Such ultrasonic excitationeffectively accelerates the bond breaking process as the tip regionpushes the cleave front forward. Therefore, with the assistance ofapplying acoustic energy the cleaving action can be much more efficientand productive. The lifetime for the mechanical blade can also beenhanced, resulting in further cost savings. Use of a pressure assistcould also reduce the binding forces on a blade approach.

Film Stress Application Conditions (P-Loading)

In certain instances, moment-only loading is insufficient to allowreliable film cleaving through large areas, and the reduction of the KIIshear stress intensity factor is necessary. There are different methodsof imparting the film stress to the crack tip such that the KII isreduced or cancelled. The thermal methods will be developed here othermethods are possible such as ultrasonic energy application in the shearmode or through the mechanical development of a force along the film(X-direction).

Based on the negative mixity from the moment loading, the thermalloading ΔT must of the correct sign to cause KI to increase and KII todecrease. Equations 9 and 10 show that this will occur if (i) a rapidcooling is imparted ahead of the crack (within the film thickness stillattached), alone or in combination with (ii) a dynamic heating on thedetached film behind the crack tip. These configurations appearidentical, as pulling on the crack tip area through the film ahead ofthe crack tip, is equivalent to pushing on the crack tip area throughthe film behind the crack tip.

Both configurations will develop a load (P) with the correct sign, butthe difference between the film being attached in front or detached inback of the crack tip will cause a significant difference in the methodsemployed to apply the loading. Here, P is the force per unit width alonga film, while lower-case (p) is the pressure behind the film in theconstant moment loading configuration.

Cleaving Utilizing Thermal Shock

According to certain embodiments, cleaving may be achieved through theaction of stress within the film layer caused by thermal differences. Inparticular, exposure of the substrate to a cooling (cold shock) mayresult in cleaving of the film. If the cooling amount is difficult froma lower temperature, a relatively long period of heating (heat soak)prior to the application of the cold shock may help increase the thermalcontrast. Alternatively, shock heating of the film behind the crack tipwill generate the stresses necessary to advance the crack under certainconditions. Both P-loading configurations are summarized in greaterdetail later in this section.

The conditions for thermally induced film stress, combine into the KIand KII equations as follows:

M=0

P=σ _(th) *h  (18)

Recognizing that a thermal stress function of magnitude α_(CTE)*E*ΔT isdeveloped by a temperature change in a material with a coefficient ofthermal expansion α_(CTE), the equation becomes,

P=α _(CTE) *E*h*ΔT  (19)

Where ΔT is the temperature difference between the film being subjectedto thermal treatment and connected material.

Substituting the thermally induced stress into equations (9 and 10)yields the following equations for KI and KII:

KI=α _(CTE) *E*h ^(1/2) *ΔT*cos(ω)/sqrt(2)  (20)

KII=α _(CTE) *E*h ^(1/2) *ΔT*sin(w)/sqrt(2)  (21)

Note that a negative sign does not precede KII.

The thermal only cleave energy equation can be derived as:

G′=2*γ′=½*α_(CTE) ² *E*h*ΔT ²*(1−υ²)  (22)

According to certain embodiments of the present invention, the action ofthe positive thermal KII and the negative moment KII can be combined, toyield a cleave propagation technique that allows simultaneousachievement of the conditions of G′=2*γ′ (or any appropriate thresholdcleave energy condition) and KII=0.

Pressure Loading (Constant M) with Cold Shock (Uncleaved Film Cold ShockLoading)

In this embodiment example, using:

P=α _(CTE) *E*h*ΔT(thermal sink from film to substrate ahead pf thecrack tip)  (23)

M=p*c ²/(4*k)(constant moment loading with a pressure source and  (24)

constraint plate)The equation for KI and KII become:

KI=α _(CTE) *E*h ^(1/2) *AT*cos(ω)/sqrt(2)+sqrt(6)*p*c ²*sin(w)/(4*k*h^(3/2))  (25)

KII=α _(CTE) *E*h ^(1/2) *AT*sin(w)/sqrt(2)−sqrt(6)*p*c ²*cos(ω)/(4*k*h^(3/2))  (26)

Solving for these equations to simultaneously satisfy the two conditions(i) G′=2*γ′, and (ii) KII=0, couples the temperature difference to thepressure in the following manner:

α_(CTE) *E*h ² *ΔT*sin(co)/sqrt(2)=6¹¹² *p*c ²*cos(ω)/(4*k)  (27)

With the second condition of 2*γ′=KI²/E′, the critical controlled cleaveconditions can be calculated as:

ΔTcrit=[2*γ′/(α_(CTE) ² *E*h*(1−υ²)*1.323)]^(1/2)  (28)

And the critical pressure to be selected to assure these conditions is:

p _(crit)=4*α_(CTE) *ΔT _(crit) *E*h ²*sin(ω)/(6^(1/2) *c²*cos(ω))  (29)

For the case where the distance (Wo) between the constraint plate andthe substrate surface is 50 p_(crit) is about 41 kPa lower than thepressure-only cleave of about 50 kPa. The critical temperature load is−183° C. (cooling).

The KII cancellation condition can be understood as follows for a 50 umsilicon film and a constraint plate placed 50 um above the surface. Inone approach, the pressure loading of 41 kPa is applied to the filmcauses the film to bend and exert a moment of about 0.0808 N-m onto thecrack tip.

A thermal cooling of −183° C. is applied close to the crack tip on theuncleaved side. As the thermal loading is applied, the KII is reducedwhile KI simultaneously increases until the fracture energy condition isreached and the crack extends. Since the extension also occurs at theconditions KII=0, the crack will extend along the cleave plane withlittle or no net tendency to move away from the cleave plane.

If the thermal loading is exceeded, the additional energy has little orno effect to change the KII=0 condition since the crack will extend atvery high speeds, about 20-40% of the speed of sound in the material.For silicon this is about 1.5 mm/usec to about 4 mm/usec. Any additionalenergy would just cool an already cleaved film material.

FIG. 6A plots cleave energy versus temperature for differential at anapplied pressure of 42 kPa. FIG. 6B plots KII/KI ratio versustemperature differential at this same applied pressure.

The combined pressure/thermal cleaving model was modeled using the AnSyssoftware and exhibited the expected functionality. Specifically,assuming an unimplanted silicon layer as a worst case, an AnSys softwaremodel has been run with the following parameters:

Wo=50 μm constraint platelength of initiated cleaved film=5 mmh=50 μmThe use of thermal heating and cooling sources was assumed.

This particular cleaving approach was modeled as a two-dimensionalstatic structural analysis with static pressure and transient thermaltemperature profiles as input loads. It was observed that the ΔT thermalloading required for KII=0 cleave propagation, was −183° C., very closeto the expected closed-form solution.

To achieve the relatively large cooling transient, a combination of aheat soak (2 msec heating to 300° C.) followed by a 30 usec coolingtransient was used to develop the desired thermal loading.

Without any heating source, the KII/KI mixity can be as high as −0.779.The pressure is set at the expected 42 kPa as calculated from the model.With application of the full temperature load and the pressure (about 6PSI) from the applied jet of gas, the initiated film is pushed upagainst the constraint plate and develops an effective length (c) of3.3-3.5 mm down to the uninitiated film. FIG. 7 shows the fully loadedpressure just prior to thermal loading.

To avoid the heating transient from causing G′ to meet or exceed thecleave fracture energy, a long thermal heating soak was used. This longsoak maintained a low temperature differential between the top andbottom of the cleave plane during the heating cycle. A soaking time of 2msec was assumed with a top temperature of 300° C. The resultant thermalprofile at the end of the 2 msec soaking time for the first zone isshown in FIG. 8A.

The thermal profile of FIG. 8A clearly shows a fairly constant verticalprofile through the film. Because of the relatively slow temperatureramp relative to the thermal time constant of the film of about 30 usec,insufficient KI and KIT components are developed within the fractureplane and the film crack does not extend.

Next, as shown in FIG. 8B, a fast cooling transient is introduced todevelop a tensile stress profile within the film to impart the necessarythermal stresses into the system. The tensile stress is made using aninstant application of a 0° C. temperature on the surface for 30 μsec,to create a thermal load of −300° C. The short time assures that thetensile stress occurs almost entirely within the film thickness (h) ononly one side of the cleave plane, and thus sufficient force P isdeveloped to exceed the cleave fracture energies. The excessive valuecompared to the threshold value of 183° C. will also serve to confirmthe ability of the process to achieve KII cancellation with a rampingthermal source that exceeds the threshold fracture energy value.

Note that using this thermal configuration, the application of thecooling transient must occur on a time scale shorter than the filmthermal time constant. For a 50 um silicon film for example, the timeconstant is about h²/D_(th) or about 36 usec (D_(th) is the siliconthermal diffusivity of about 0.7 cm²/s). The cold shock can be appliedusing a stream of cryogenic liquid, solid or gas with enough heattransfer characteristics. Carbon dioxide snow (CO₂) or liquid nitrogenare two examples of source of the cold shock. Alternatively, the coldshock time constant can be relaxed (lengthened) by pre-heating the brickas appropriate, to induce the desired effective temperaturedifferential.

FIG. 8B shows the thermal profile after this cooling transientapplication. The advantageous thermal profile of the tensile stress ofthe film results in the desirable KII=0 condition.

Using an applied pressure of 42 kPa, the crack propagation will occur atKII=0 once sufficient tensile stresses exist. For the more complicatedthermal profile modeled here, the profiles of p and of temperature maybe necessary to match the energy and KIT cleave conditions usingreal-world approaches to heating and cooling.

The cleaving that occurs is controlled, and exhibits a double-stepcleaving progression where the heating cycle does not propagate thecleave. The brief cooling transient causes the crack front to propagateto the next zone. FIGS. 9A-D show the heating/cooling cleaving sequencemodeled by the AnSys software. The shear stress pictures show the cleavelocation and crack tip stresses clearly. Note that the heating cycleshows a lower positive shear, indicative of the lack of cleave energyavailable for propagation.

The application of a thermal load of this type can progress throughsuccessive scanning of the thermal load sequence, to propagate thecleave and separate a progressively larger portion of the film. Thus, anadvantage of a constant moment loading is that after the application ofthe desired moment, the propagation keeps the moment at the desiredvalue independent of the location of the cleave front.

FIG. 10 plots several values on a linear scale, as a function ofdistance (in μm) of the centroid of the zone from the tab edge of thesubstrate. FIG. 10 shows a first order reduction in KII as compared withthe result of FIG. 5 above in the non-temperature (P=0) case. The FIG.10 shows that KI is now the major stress intensity contributor to crackenergy with D1 almost equal to the cleave energy 2*γ′ or 2.4 J/m². Themixity KII/KI and D2 are very low, thus confirming the action of thecancellation configuration.

As shown in the model, cleaving progresses rapidly and controllablythrough each zone. Although the latter zones are 250 μm in length, thiscan be increased without compromising the cracking behavior, so long asthe pressure be maintained as the cleave front propagates and the volumeof the fracture increases as a result.

According to particular embodiments, scanning of the heat soak/coldshock sources could allow continuous propagation of the cleave front.For example, if 10 msec is used to cover a length of material of 250 um,a 156 mm tile could be cleaved in about 6 seconds. This assumes that thethermal and pressure loading is applied across a width of the tile, andlinearly scanned at a rate of about 2.5 cm/sec.

While the above embodiments describe the performance of cleaving byapplication of a constant pressure in conjunction with repeatedapplication of a thermal shock, this is not required by the presentinvention. In accordance with particular embodiments, the magnitude ofthe applied pressure can be changed to achieve desired cleavingproperties.

Thermal Heating Shock Cleaving

Instead of using a cooling thermal shock ahead of the crack tip, aheating shock can be applied on the film behind the crack tip. To allowthe thermal shock to efficiently develop P in this configuration, thethermal application develops the shock wave before there is a mechanicalrelaxation of the expansion through movement of the film away from thecrack tip area.

In contrast with the cooling configuration where the thermal shock timeis linked to the thermal time constant of the film, the film heatingconfiguration is applied on a time scale on the same order as theacoustic time constant of the film material. The rapid heating istherefore applied in a very short time interval on the range of sub 100nanoseconds to a few microseconds, depending on the width of the heatshock and its proximity to the crack tip.

To achieve the threshold crack propagation condition (ΔT=183° C.), forexample on 50 um silicon within 250 nsec, a power density of over 6MW/cm² is required. This is a very high power density that is within theadiabatic heating regime of silicon.

To avoid generating heating stresses along the depth of the silicon filmthat can lead to damage in the form of pits, surface melting, filmbreakage and cracking, volumetric heating is preferable over surfaceheating. Electron beam (E-Beam) heating is a good candidate technologyto apply to this heating, as it can volumetrically heat a portion of thefilm (cleaved or uncleaved).

E-beams are also highly controllable with the following generalcharacteristics. E-Beams allow beam scanning over a large area with highcontrollability and speed. E-Beams allow fine control over beamintensity and diameter (micron to centimeter size). E-Beams allowcontrol over pulsing from nanoseconds to CW. E-beams allow control overheating depth by changing electron beam energy (keV to MeV,corresponding to beam penetration ranges from a few microns to a fewcentimeters—see FIG. 11).

The power flux of the beam is therefore easily controlled by selectingthe beam diameter, beam energy and beam intensity while the penetrationrange is selected by the beam energy. For example, 50 um electron beampenetration in silicon is about 80 keV and a 0.5 mm beam diameter wouldrequire a 200 mA beam intensity pulse for 250 nsec. Alternatively, apulsed beam treatment could be made with a CW beam scanned sufficientlyrapidly. For the example above, the required beam scan velocity would be0.5 mm/250 nsec or 200,000 cm/sec. Most if not all of the abovecharacteristics can be available in present system built for precisionvacuum welding and material modification applications. For example,e-beam systems from Pavac Industries, Inc. (Richmond, B. C. Canada,www.pavac.com) and others could be used as an adiabatic heating source.

E-beams could control the propagation of the crack tip under KIIcancelling configurations. E-beam technology can also be used forinitiating a first area of film as well as possibly cleaving under pureshear conditions. These approaches are described below.

Control of Cleave Depth Using KII Canceling

Maintaining precise control over film thickness is important not onlyfor achieving highly uniform films, but also to avoid cleave failures.The KII canceling scheme offers the inherent ability to control thepropagating cleave depth, by modulating the applied moment as a functionof active depth control feedback.

Equations 25 and 26 describe how KI and KII stress intensity factorschange with applied loading. A rise of p will increase M, and thus causean extending crack to become shallow as the cleaving propagates moretowards the surface. Conversely, a lower p will require more thermalenergy to achieve the fracture condition and move the crack deeper.Control over depth could therefore be made by modulating the pressure pwhile the crack is propagating to achieve the desired depth. Thissuggests that reduced dose or even no dose propagation is possible usingthis technology.

Applicability to Other Cleave Configurations than KII=0

While embodiments have been described above in connection with pressurecleaving in combination with the use of a thermal shock, this is notrequired by the present invention. In accordance with alternativeembodiments, the cleave sequence could be modified such that theA_(KII)− and A_(KII+) factors are particularly high and can effectivelyguide the fracture propagation throughout the cleave sequence. In suchembodiments, a single loading energy source (pressure or thermal) candrive the cleaving with non-zero KII. In such embodiments, the use ofpulsed (time varying) pressure or scanning thermal/cooling sources couldstill confer controllability in cleave propagation. For example, a laserheating source could be used to generate a −P1 force to generate sheardominant (KII dominant) cleave conditions. The laser energy can beinjected through heating of the silicon material ahead of the crack tip,as well as heating the film directly behind the crack tip and allowingheat conduction to further heat the specific crack tip area. Althoughthe stress intensity mixity would favor crack propagation towards thesurface, film compression due to the heating process would help todiscourage propagation within the film and force shear-dominantpropagation along the cleave plane.

Use of Thermal Shock Technologies for Film Initiation

The use of a patterned implant was described above in connection withallowing the lowest total dose film cleaving process. In the proposedprocess sequence, film initiation would be made on a higher dose area topartially release a film of a few millimeters in width. This partiallyreleased film can in turn can be used to propagate the balance of thecleaving under KIT cancellation or other methods of film propagation.

The E-beam technology, laser or flashlamp technologies, could be used todetach the film from the substrate. The E-beam technology may beparticularly suited for this purpose, as the energy range could beadjusted to allow film temperature to rise volumetrically within theinitiation area close to the edge of the substrate. The pulsed energywould deposit over time within the film thickness, an almost constant ΔTrise in temperature, with a sharp change in temperature profile adjustedto be located at or near to the cleave plane.

Such adiabatic heating of silicon by E-beam exposure is shown in FIG.13, which plots energy density versus depth into silicon, for E-beamirradiation over a time period where some temperature averaging occurredwithin the film volume. According to particular embodiments of thepresent invention, the abrupt change in temperature gradient resultingfrom adiabatic E-beam heating may comprise a change of greater than 10°C./μm.

For example, a 250 nsec pulse would only diffuse the thermal profile byabout 5 um, substantially less than the film thickness. This wouldgenerate a shear cleave that would limit the presence of thermal shocksacross the thickness of the film, and produce a large shear that cancontrollably cleave the film. The initiation cleaving could start at anedge and be extended to cover the desired film width to support thepropagation cleave method. Alternatively, the initiation cleaving couldstart at an interior location and then extend to the periphery. If aninternal initiation cleaving is used, a vacuum environment would benefitthe cleaving process by reducing the energy needed for film bucklingsince there will not be any appreciable pressure developing a restoringforce to the upwards film movement.

Use of Thermal Shock Technologies for Film Propagation

An intense thermal shock pulse in combination with constant volumetricheating characteristics could also be used to propagate the film fromthe initiation region. With E-beam technology in particular, a fastpulse application that can heat the film thickness uniformly, couldallow the controlled propagation of the film by pure shear cleaving orwith a moment assist. The use of E-Beam technology for cleaving of filmsis described in U.S. Pat. No. 6,013,563, which is incorporated byreference in its entirety herein for all purposes. In accordance withparticular embodiments of the present invention, the E-Beam radiationmay be applied in a direction perpendicular to a face of the substrate.

The matching of the E-beam volumetric heating (end of range or Rp) canbe made by selecting a higher or lower energy e-beam. The E-beam energycan be selected so that its Rp is about the thickness of the film to becleaved, although in practice an effective control of the cleave depthmay have some offset between the cleave depth and Rp.

The use of E-beam radiation may be particularly favored here because theenergy range could be adjusted to allow a film temperature risevolumetrically within the propagation area close to the crack tip, butjust within the uncleaved area. The pulsed energy would deposit withinthe film thickness an almost constant ΔT rise in temperature, with asharp change in temperature profile adjusted to be at or near to thecleave plane.

For example, a 250 nsec pulse would only diffuse the thermal profile byabout 5 um, substantially less than the film thickness. This wouldgenerate a shear cleave that would limit the presence of thermal shocksacross the thickness of the film and produce a large shear that cancontrollably cleave the film.

To quantify this regime, the KI and KII equations 26 & 27 can bemodified with p=0 and to yield the following relations:

KI=α _(CTE) *E*h ^(1/2) *ΔT*cos(ω)/sqrt(2)  (30)

KII=α _(CTE) *E*h ^(1/2) *ΔT*sin(ω)/sqrt(2)  (31)

The thermal only cleave energy equation can be derived as:

G′=2*γ′=½*α_(CTE) ² *E*h*ΔT ²*(1−υ²)  (32)

For KII shear cleaving, the required thermal heating across h istherefore:

ΔT=[4*γ′/α_(CTE) ² *E*h*(1−υ²)]^(1/2)  (33)

As an example, a 50 um silicon layer with 1.2 J/m² would require about300° C. of near-instantaneous temperature rise. Assuming about 0.7J/cm²-° C., the required energy deposition on the silicon surface isabout 2.44 J/cm². Using an 80 keV E-beam pulse with a 0.5 mm×0.5 mm beamspot and 250 nsec beam pulsewidth, for example, corresponds to a beamintensity of about 300 mA. This is well within current E-beamtechnology.

If a moment is added, the G′ equation is modified to:

G′=2*γ′=½*α_(CTE) ² *E*h*ΔT ²*(1−υ²)+6*(1−υ²)*M ² /E*h ³  (34)

This equation shows that the use of a moment is additive and will reducethe temperature ΔT needed to achieve the crack extension condition.

The AnSys software was used to confirm this cleave propagation mode.FIG. 12A-C shows a 50 um silicon film cleave FEA static structuralsimulation. In FIG. 12A, a moment M=0.08 N-m was applied on the startingfilm (on the first 500 um film segment). A positive temperature ramp onthe film was started and led to buckling decohesion of the film. FIG.12C shows the cleave propagating to the end of the heated zone.

With a moment of 0.08 N-m, the ΔT onset of propagation was calculatedfrom equation 35 as 180° C. This agrees very well with the Ansys valueof 176° C. By contrast, absent a moment, the value is about 300° C.These results show that buckling film decohesion (moment assisted ornot) is a practical cleave configuration.

The use of E-beam heating methods would be beneficial in this mode,since the rapid adiabatic heating will give a sharp compressive stressprofile that can help guide the propagating cleave. Cleave depth couldalso be controlled by altering the E-beam energy, thus changing thethickness of the film that is subjected to volumetric heating.

Selection of the heated zone width was also confirmed to yield controlover cleave extension. The heated zone width will dictate, to firstorder, the amount of crack extension that will occur upon the heatingcycle. This is because after the cleave front has reached the edge ofthe heated cleave area, G′ will drop and the propagating cleave willarrest.

Lastly, any of the heating techniques used in conjunction with animplanted cleave layer could help use the implant induced stresses moreefficiently. This would occur by the higher temperature, which would inturn increase the implant stresses (these are usually proportional tokT). A heated pulse could therefore have a secondary, favorable effecton the cleave plane, enhancing stresses in the cleave plane for betterguidance of cleave propagation.

If a cleave propagation action occurs with fracture energy G′ at leastpartly comprising release of a stored positive moment energy (forexample with a hydrogen cleave plane with the compressive layer situatedat the bottom of the film), a vacuum environment could benefit thecleaving process. Specifically, a vacuum environment could allow formore efficient release of energy, as there will not be any appreciablepressure developing a restoring force to the upward film movement. Forexample, if a thermal shear cleave mode is employed, the use of a vacuumwill also tend to reduce the negative KI stress intensity that is knownto potentially increase fracture toughness (effective fracture energyG′). It is worthy of noting that high vacuum conditions are notrequired, and even a partial vacuum of many Torrs could demonstrate thiseffect.

The continuation of the cleave process would eventually result acomplete lift off of a thick film along the cleave region, out of theremaining portion of the semiconductor substrate. In one embodiment,this remaining portion with a newly exposed surface region, is incondition for repeating the cleaving method by again performing thecleave initiation and propagation methods.

A cleavage plane of lower surface energy may be selected as the surfaceregion for the semiconductor substrate. Thus, in an embodiment, afterone thick film is lifted off from the substrate, a new surface planewould be substantially in the original crystallographic plane and in agood condition, with relatively small surface roughness for additionallayer transfer production without need of complicated surface treatmentlike etching or polishing.

Of course, there can be other variations, modifications, andalternatives. Depending upon the embodiment, the processes can be forthe formation of photovoltaic cells, integrated circuits, opticaldevices, any combination of these, and the like.

Consideration of M₂/P₂ and M₃/P₃ Factors in Cleaving

Returning to FIG. 2, equation (6) is again reproduced below.

$\begin{matrix}{G^{\prime} = {\frac{1}{2\overset{\_}{E}}\left\lbrack {\frac{P_{1}^{2}}{h} + {12\frac{M_{1}^{2}}{h^{3}}} + \frac{P_{2}^{2\;}}{H} + {12\frac{M_{2}^{2}}{H^{3}}} - \frac{P_{3}^{2}}{h + H} - {12\frac{M_{3}^{2}}{\left( {h + H} \right)^{3}}}} \right\rbrack}} & (6)\end{matrix}$

In this equation (6), terms three through six may also be considered indesigning a process to achieve desirable cleaving of a film from aworkpiece such as a tile or substrate.

For example, forces P₂, M₂, P₃, and M₃ may be exerted in a number ofways during cleaving. According to certain techniques, the tile may befixed in position while it is subjected to processes that generatetensile and/or compressive stress in the tile.

In certain embodiments, the tile could be fixed in position by clampingthe ends of the tile. In such an embodiment, a clamp could engage anotch or groove present in the side of the tile. Such a notch or groovemay be intentionally machined in the tile for this purpose.

In other embodiments, the tile could be fixed in position by securingthe tile from below, for example by electrostatic or vacuum chucking. Instill other embodiments, a tile could be secured from both the bottomand the sides. In these embodiments, efficient generation oftile/substrate M and P terms could require the clamping or fixing methodto allow for the generation or control of one or more of P2, M2, P3, andM3.

Any one of a number of techniques could be employed to generate thedesired tensile and/or compressive stresses within the tile. Forexample, as shown in FIG. 14, one approach is to clamp the tile 1402 inplace, while directly applying force(s) F to the tile edge(s). Thisapproach could generate directly in the tile, moments M₂ and M₃ (andassociated P₂ and P₃) of sufficient magnitude to significantly influencethe equation (6).

Another approach is to generate a local temperature gradient ofsufficient intensity, that differences in expansion at various depths inthe tile give rise to the requisite strain. Such an approach isillustrated in FIG. 15, where a localized thermal gradient 1500 isgenerated in clamped tile 1502 by application of a laser beam 1504.

As shown in FIG. 15, thermal gradient 1500 is sufficiently distant frompoint C of the front at which cleaving is taking place, that thetemperature from the laser does not itself influence cleaving energy.More specifically, the energy from the thermal gradient does notappreciably affect the magnitude of the term P of equation (19).Instead, the energy is coupled through to the crack by stresses andmoments generated from the laser-induced heated volume situated somedistance away for the crack tip.

However, as a result of application of the laser, material at differentdepths in the tile experience different amounts of thermal expansion.This difference in thermal expansion versus depth, in turn can give riseto compressive stress of sufficient magnitude to generate a moment M₃that influences the equation (6).

While the embodiment of FIG. 15 shows generation of the thermal gradientby application of a laser to the top surface of the tile, this is notrequired. In accordance with other embodiments, a thermal gradient ofdesired intensity could be generated by the application of energy inanother form, such as an electron beam. Moreover, energy could beapplied to other surfaces of the tile, including the sides or thebottom. Moreover, the energy applied to the tile need not be limited toa single source having local effect. In accordance with otherembodiments, a global increase in temperature of the tile (such as apulsed heating of the top or bottom surface) can contribute partially orwholly to the initiation and/or propagation of a cleave front.

Still another approach to generating moments M₂/M₃ to achieve cleaving,is through the application of sonic energy. Some embodiments of suchapproaches are illustrated in FIGS. 16-17.

FIG. 16 shows a simplified schematic view of one embodiment, whereintransducer 1600 is separated from tile 1602 by medium 1604. Sonic energy1606 from transducer 1600 is applied to the clamped tile 1602 throughmedium 1604, which may be air, but may alternatively comprise a liquidor other gas to enhance coupling of the sonic energy to the tile.

Sonic energy impacting the tile gives rise to oscillation by the tile.Where the character (i.e. frequency, wavelength) of the applied sonicenergy matches harmonics of the tile, resonant energy can rapidly buildup in the tile.

Such oscillation is shown in FIG. 16. In particular, As shown in thisfigure, sonic energy impacting the tile gives rise to oscillation by thetile, including the partially detached film, portions underlying thepartially detached film, and portions of the tile that have not yet beencleaved. Such oscillations in turn create both positive and negativemoments (respectively M₁, M₂, and M₃) that may be of a sufficientmagnitude to influence cleaving. Moreover, such energy build up isparticularly likely in the solid, crystalline materials that aregenerally the target of cleaving, as those solid crystalline materialstypically exhibit a large quality (Q) of resonance.

Detection of the harmonics in a tile is straightforward. As shown inFIG. 16, a microphone 1610 may be placed in contact with or proximate totile 1602. Input from the microphone may be input to host computer 1614comprising processor 1616 in communication with a computer-readablestorage medium 1618.

Controller 1612 scans the frequency of sonic energy emitted by thetransducer. Matching of the frequency of applied sonic energy with aharmonic of the tile, is revealed by emission of a sound of particularlyhigh intensity by the microphone. Such a particularly high intensitysound may be indicated by one of the peaks 1620 shown on display 1622that is in electronic communication with host computer 1614.

While FIG. 16 shows an embodiment wherein the transducer is sonicallycoupled to the tile through a medium, this is not required. In analternative embodiment, a transducer may be in direct physical contactwith the tile in order to give rise to cleaving.

Moreover, while FIG. 16 shows an embodiment wherein sonic energy isapplied globally to the tile, this is also not required. For example, asshown in the alternative embodiment of FIG. 17, the transducer 1750 maybe smaller than the tile 1752, and positioned to apply sonic energydirectly to only a portion thereof. In some embodiments, the transducermay be configured to move across the surface of the tile to providesonic energy at or in front of an advancing the cleave front.

The development of moments and forces M₂/M₃ and P₂/P₃ can be selected ina static fashion (clamp or bending), or in an oscillatory fashion (suchas with the use of sonic or ultrasonic transducers) in a manner wherethe local crack tip stress intensity KI and KII is adjusted to lower,cancel or control KII. These external forces and moments can thus notonly add energy to the crack tip, but if properly selected can also helpcontrol propagation within a desired cleave plane. For example, bendingthe tile in a +M₂ and −M₃, or heating the tile bottom in a pulsedfashion will generate a +KII component that could help cancel KII.

While the above description focuses upon the application of a thermalshock utilizing localized application of thermal energy to the surfacefollowed by localized cooling of the surface, this is not required. Incertain embodiments, the desired conditions could be achieved by globalapplication of one or both of the thermal energy or the cooling. And, incertain embodiments, the thermal energy and/or the cooling could beapplied to a location other than the surface, for example a backside ofa wafer or a side of the wafer. Moreover, in certain embodiments,cooling alone could be employed to achieve the desired result, whetherin the active application of negative thermal energy, or in the passivedissipation of heat through the substrate material and/or into thesurrounding environment.

While the above is a full description of the specific embodiments,various modifications, alternative sequences and devices may be used.For example, while the use of a vacuum force to peel away the cleavedfilm was described above in connection with a constraint plate, this isnot required, and an electrostatic force could be used. In accordancewith alternative embodiments, a vacuum force or an electrostatic forcecan be employed in an absence of a constraint plate, to draw the cleavedfilm away from the remaining substrate as the cleave front advances.

FIG. 18 shows a simplified flow diagram illustrating steps of a process1800 to achieve cleaving employing sonic energy in accordance with anembodiment of the present invention. In a first step 1802, the tile issecured to a support, such as a chuck or side clamping. In a second step1804, the secured tile is placed in sonic communication with atransducer. In a third step 1806, a microphone is placed incommunication with the tile. In a fourth step 1808, a frequency of sonicenergy emitted by the transducer is scanned over a range. In a fifthstep 1810, the microphone is used to detect a sound emission profile ofthe substrate over the scanned frequency range. In a sixth step 1812,peaks in the sound emission profile are correlated with harmonics of thesecured tile. In a seventh step 1814, the transducer is configured toemit sonic energy of a frequency known to correlate with one or moreharmonics of the secured substrate, in order to promote cleaving of afilm from the substrate.

Although the above has been described using a selected sequence ofsteps, any combination of any elements of steps described as well asothers may be used. Additionally, certain steps may be combined and/oreliminated depending upon the embodiment.

The type of ionic particles that are implanted to form a cleave regioncan be varied from hydrogen ions to helium ions, deuterium ions, orcertain combinations to allow for formation of the cleave regionaccording to alternative embodiments.

Still further, the cleaving process may include temperaturecontrolled/assisted cleaving utilizing vacuum chucking or electrostaticchucking process. Of course there can be other variations,modifications, and alternatives.

Therefore, it is also understood that the examples and embodimentsdescribed herein are for illustrative purposes only and that variousmodifications or changes in light thereof will be suggested to personsskilled in the art and are to be included within the spirit and purviewof this application and scope of the appended claims.

What is claimed is:
 1. A method for cleaving a film of material, themethod comprising; providing a substrate having a face and an underlyingcleave region; applying a thermal source having a predetermined energyin a direction perpendicular to the face to create a volume of heatedmaterial between the cleave region and the face, the heated volumeexhibiting a substantially uniform temperature profile followed by asharp drop in temperature at the cleave region; and cleaving the filmfrom the substrate at the cleave region.
 2. The method of claim 1wherein application of the thermal source heats the volume of materialin an adiabatic process.
 3. The method of claim 1 wherein the sharp dropin temperature is 10° C./μm or greater.
 4. The method of claim 1 whereinthe thermal source is a photon source.
 5. The method of claim 4 whereinthe photon source comprises a laser.
 6. The method of claim 1 whereinthe sharp drop in temperature results in a controlled shear at thecleave region.
 7. The method of claim 6 wherein the thermal sourcecomprises a laser scanned with a propagating crack to generate sheardominant cleave conditions within the cleave region.
 8. The method ofclaim 6 wherein: the thermal source is applied at a distance ahead ofthe crack; a thermal gradient arises from the substantially uniformtemperature profile followed by the sharp drop in temperature; andenergy from the thermal gradient is coupled across the distance throughto the crack by moments and stresses within the cleave region.
 9. Themethod of claim 1 wherein the cleaving comprises applying a pressure topropagate a crack in the cleave region.
 10. The method of claim 9further comprising modulating the pressure to control a depth of crackpropagation.
 11. The method of claim 9 wherein the pressure is appliedby a jet of gas or by insertion of a blade.
 12. The method of claim 1wherein the thermal source is an energetic electron beam source.
 13. Themethod of claim 12 wherein the thermal source comprises a plurality ofenergetic electrons applied in a vacuum environment having a pressure ofbetween about 10⁻⁴ to 10⁶ Torr.
 14. The method of claim 12 wherein avacuum environment facilitates the cleaving.
 15. The method of claim 12wherein the energetic electron beam source causes a temperature risevolumetrically within an uncleaved propagation area close to a crack.16. The method of claim 1 further comprising fixing the substrate inposition during application of the thermal source and the cleaving. 17.The method of claim 16 wherein fixing the substrate in positioncomprises clamping edges of the substrate.
 18. The method of claim 16wherein fixing the substrate in position comprises securing thesubstrate from below.
 19. The method of claim 1 further comprisingbending the substrate during application of the thermal source and thecleaving.
 20. The method of claim 1 further comprising heating thesubstrate from below during application of the thermal source and thecleaving.